Rotations, step by step

A rotation turns a point about the origin, and the quarter turns are the ones with clean coordinate rules.

The question
(2, −2)90° counterclockwise about O ()

(2, −2) 90° counterclockwise about O

(2, −2)
2, −2swap−2, 2
(2, −2)(2, 2)
  1. Start where the point is: (2, −2). The move is 90° counterclockwise about O, and the question is only where those two numbers end up.
  2. A quarter turn SWAPS the two numbers — going 2 across and −2 up becomes going −2 across and 2 up — and then one of them changes sign, because the turn carries the point into a different quarter of the grid.
  3. Turning counterclockwise, that gives (2, 2).

How it works.

  1. 01

    Start where the point is: (2, −2). The move is 90° counterclockwise about O, and the question is only where those two numbers end up.

  2. 02

    A quarter turn SWAPS the two numbers — going 2 across and −2 up becomes going −2 across and 2 up — and then one of them changes sign, because the turn carries the point into a different quarter of the grid.

  3. 03

    Turning counterclockwise, that gives (2, 2).